Stan's cookie recipe makes $24$ cookies and calls for exactly $384$ sprinkles. He is wondering how many sprinkles $(p)$ he will need to make $60$ cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make $60$ cookies?
Solution: We can set up a proportion like this: $\dfrac{\text{Sprinkles needed for 24 cookies}}{\text{Sprinkles needed for 60 cookies}} = \dfrac{\text{24 cookies}}{\text{60 cookies}}$ Substituting values from the problem, we get this: $\dfrac{384 \text{ sprinkles}}{p\text{ sprinkles}} = \dfrac{24 \text{ cookies}}{60\text{ cookies}}$ Let's solve for $p$ : $\dfrac{384 \text{ sprinkles}}{p\text{ sprinkles}} = \dfrac{24 \text{ cookies}}{60\text{ cookies}}$ $60 \cdot 384 = 24 \cdot p $ $23{,}040 = 24p$ $p = \dfrac{23{,}040}{24}~~~~~~~~~~~$ Divide both sides by $24$. $p = 960$ Stan needs $960$ sprinkles to make $60$ cookies.